<PAGE>   1
                     U.S. SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   FORM 10-QSB

(Mark One)

 X       QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES 
---      EXCHANGE ACT OF 1934
         For the quarterly period ended:  March 31, 1998
                                         ---------------

         TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
---      EXCHANGE ACT OF 1934 
         For the transition period from _______________ to ________________

                        Commission file number: 33-43317
                                                --------

                              EASTON BANCORP, INC.
    ------------------------------------------------------------------------
        (Exact name of small business issuer as specified in its charter)

                Maryland                             52-1745344
       ------------------------          ------------------------------------
       (State of incorporation)          (I.R.S. Employer Identification No.)

                   501 Idlewild Avenue, Easton, Maryland 21601
                   -------------------------------------------
                    (Address of principal executive offices)

                                 (410) 819-0300
                                 --------------
                           (Issuer's telephone number)

                                 Not Applicable
--------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                         if changed since last report)


         Check whether the issuer: (1) filed all reports required to be filed by
Section 13 or 15(d) of the Exchange Act during the past 12 months (or for such 
shorter period that the registrant was required to file such reports), and (2) 
has been subject to such filing requirements for the past 90 days. 
Yes X No
   ---  ---

         State the number of shares outstanding of each of the issuer's classes
of common equity, as of the latest practicable date:

         On May 8, 1998, 560,318 shares of the issuer's common stock, par value
$.10 per share, were issued and outstanding.

         Transitional Small Business Disclosure Format (check one): Yes   No X
                                                                       ---  ---
<PAGE>   2
                                     PART I
                              FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS.

                       EASTON BANCORP, INC. AND SUBSIDIARY
                           CONSOLIDATED BALANCE SHEETS
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                  March 31,        December 31,
                                                                    1998               1997
                                                                    ----               ----
<S>                                                             <C>                <C>         
                                     ASSETS
Cash and due from banks                                         $  1,006,941       $    642,726
Federal funds sold                                                 4,342,286          3,739,622
Investment in Federal Home Loan Bank stock                           145,600            124,500
Investment securities held-to-maturity (market
  value of $1,501,967 and $1,502,794, respectively)                1,500,097          1,500,000
Loans, less allowance for credit losses of
  $387,400 and $378,000, respectively                             34,845,689         34,682,279
Premises and equipment, net                                        1,689,070          1,713,683
Intangible assets, net                                                11,741             30,261
Accrued interest receivable                                          202,687            248,303
Other assets                                                          64,394             58,323
                                                                ------------       ------------
           Total assets                                         $ 43,808,505       $ 42,739,697
                                                                ============       ============

                      LIABILITIES AND STOCKHOLDERS' EQUITY
Deposits
  Noninterest-bearing                                           $  1,910,690       $  2,060,848
  Interest-bearing                                                37,243,666         36,027,304
                                                                ------------       ------------
           Total deposits                                         39,154,356         38,088,152
Accrued interest payable                                             101,332             99,980
Securities sold under agreements to repurchase                       484,755            481,490
Other liabilities                                                     26,251             57,363
                                                                ------------       ------------
           Total liabilities                                      39,766,694         38,726,985
                                                                ------------       ------------

Stockholders' equity
  Common stock, par value $.10 per share;
    authorized 5,000,000 shares; 559,478
    and 559,328 shares issued and outstanding,
    respectively                                                      55,948             55,933
  Additional paid-in-capital                                       5,219,171          5,217,686
  Retained earnings (deficit)                                     (1,233,308)        (1,260,907)
                                                                ------------       ------------
           Total stockholders' equity                              4,041,811          4,012,712
                                                                ------------       ------------
           Total liabilities and stockholders' equity           $ 43,808,505       $ 42,739,697
                                                                ============       ============
</TABLE>


See accompanying Notes to Consolidated Financial Statements.



                                       1
<PAGE>   3
                       EASTON BANCORP, INC. AND SUBSIDIARY
                        CONSOLIDATED STATEMENTS OF INCOME
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                          Three Months Ended
                                                                March 31,
                                                         ---------------------
                                                         1998             1997
                                                         ----             ----
<S>                                                    <C>              <C>     
Interest revenue
  Loans, including fees                                $752,408         $686,678
  Investment securities                                  24,552           19,079
  Federal funds sold                                     52,700           48,393
                                                       --------         --------
         Total interest revenue                         829,660          754,150

Interest expense                                        448,055          379,292
                                                       --------         --------

         Net interest income                            381,605          374,858

Provision for loan losses                                36,533           21,858
                                                       --------         --------

         Net interest income after
           provision for loan losses                    345,072          353,000
                                                       --------         --------

Other operating revenue                                  26,761           29,126
                                                       --------         --------

Other expenses
   Salaries and benefits                                204,318          174,186
   Occupancy                                             13,521           20,529
   Furniture and equipment                               24,901           24,375
   Other operating                                      101,494           99,280
                                                       --------         --------
         Total operating expenses                       344,234          318,370
                                                       --------         --------

Net income before income taxes                           27,599           63,756

Income taxes                                                 --               --
                                                       --------         --------

Net income                                             $ 27,599         $ 63,756
                                                       ========         ========

Earnings per common share - basic                      $   0.05         $   0.11
                                                       ========         ========

Earnings per common share - diluted                    $   0.05         $   0.11
                                                       ========         ========
</TABLE>


See accompanying Notes to Consolidated Financial Statements.


                                       2
<PAGE>   4
                       EASTON BANCORP, INC. AND SUBSIDIARY
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                       Three Months Ended
                                                                            March 31,
                                                                       ------------------
                                                                      1998              1997
                                                                  -----------       -----------
<S>                                                               <C>               <C>        
CASH FLOWS FROM OPERATING ACTIVITIES
  Interest received                                               $   862,718       $   722,286
  Other revenue received                                               27,795            29,346
  Cash paid for operating expenses                                   (337,275)         (410,649)
  Interest paid                                                      (446,703)         (377,678)
                                                                  -----------       -----------
                                                                      106,535           (36,695)
                                                                  -----------       -----------
CASH FLOWS FROM INVESTING ACTIVITIES
  Cash paid for premises and equipment                                 (2,043)           (4,825)
  Net loans to customers                                             (187,382)           36,209
  Investment securities purchased                                    (271,200)         (502,900)
  Proceeds from sales/maturities of investments                       250,000           500,000
  Loan participations sold                                                 --           111,795
                                                                  -----------       -----------
                                                                     (210,625)          140,279
                                                                  -----------       -----------
CASH FLOWS FROM FINANCING ACTIVITIES
  Net change in customer deposits                                   1,066,204         1,631,767
  Proceeds from stock options exercised                                 1,500                --
  Net change in securities sold under agreements to
     repurchase                                                         3,265           240,247
                                                                  -----------       -----------
                                                                    1,070,969         1,872,014
                                                                  -----------       -----------

NET INCREASE IN CASH                                                  966,879         1,975,598
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                    4,382,348         4,035,909
                                                                  -----------       -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD                        $ 5,349,227       $ 6,011,507
                                                                  ===========       ===========

RECONCILIATION OF NET INCOME TO NET CASH
   PROVIDED (USED) IN OPERATING ACTIVITIES
   Net income                                                     $    27,599       $    63,756
   Adjustments to reconcile net income to net cash
     provided (used) in operating activities:
       Depreciation and amortization                                   40,809            38,543
       Provision for loan losses                                       36,533            21,858
       Decrease (increase) in accrued interest receivable
         and other assets                                              43,912           (35,229)
       Increase (decrease) in operating accounts payable
         and other liabilities                                        (29,760)         (124,590)
       Increase (decrease) in deferred loan origination fees          (12,561)           (1,033)
                                                                  -----------       -----------
                                                                  $   106,532       $   (36,695)
                                                                  ===========       ===========

Noncash activity:
   Other real estate acquired through foreclosure                 $        --       $        --
                                                                  ===========       ===========
</TABLE>

See accompanying Notes to Consolidated Financial Statements.


                                       3
<PAGE>   5
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS:

1.       Basis of Presentation

         The accompanying unaudited condensed financial statements have been
prepared in accordance with generally accepted accounting principles for interim
financial information and with the instructions to Form 10-QSB and Item 310(b)
of Regulation S-B of the Securities and Exchange Commission. Accordingly, they
do not include all the information and footnotes required by generally accepted
accounting principles for complete financial statements. In the opinion of
management, all adjustments (consisting of normal recurring accruals) considered
necessary for a fair presentation have been included. Operating results for the
three months ended March 31, 1998, are not necessarily indicative of the results
that may be expected for the year ended December 31, 1998. For further
information, refer to the consolidated financial statements and footnotes
thereto for the Company's fiscal year ended December 31, 1997, included in the
Company's Form 10-KSB for the year ended December 31, 1997.

2.       Cash Flows

         For purposes of reporting cash flows, cash and cash equivalents include
cash on hand, unrestricted amounts due from banks, overnight investments in
repurchase agreements, and federal funds sold.

3.       Adoption of New Accounting Principles

         During the fourth quarter of 1997, the Company adopted Financial
Accounting Standards Board Statement No. 128, "Earnings Per Share." SFAS 128
replaces the presentation of primary earnings per share with a presentation of
basic earnings per share and it requires a dual presentation of basic and
diluted earnings per share on the face of the income statement. SFAS 128 was
effective for financial statements issued for periods ending after December 15,
1997. The adoption of this pronouncement by the Company in 1997 has resulted in
the recalculation and restatement, where necessary, of the Company's prior
period earnings per share disclosures. The Company's earnings per share for the
quarters ended March 31, 1997 and March 31, 1996, were unchanged when
recalculated in accordance with SFAS 128, and thus there is no restatement of
these prior period earnings per share disclosures in this Form 10-QSB.




                                       4
<PAGE>   6
         This Report contains statements which constitute forward-looking
statements within the meaning of Section 27A of the Securities Act of 1933 and
Section 21E of the Securities Exchange Act of 1934. These statements appear in a
number of places in this Report and include all statements regarding the intent,
belief or current expectations of the Company, its directors or its officers
with respect to, among other things: (i) the Company's financing plans; (ii)
trends affecting the Company's financial condition or results of operations;
(iii) the Company's growth strategy and operating strategy; and (iv) the
declaration and payment of dividends. Investors are cautioned that any such
forward-looking statements are not guarantees of future performance and involve
risks and uncertainties, and that actual results may differ materially from
those projected in the forward-looking statements as a result of various factors
discussed herein and those factors discussed in detail in the Company's filings
with the Securities and Exchange Commission.

ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS.

         Easton Bancorp, Inc. (the "Company") was incorporated in Maryland on
July 19, 1991, primarily to own and control all of the capital stock of Easton
Bank & Trust Company (the "Bank") upon its formation. The Bank commenced
business on July 1, 1993, and the only activity of the Company since then has
been the ownership and operation of the Bank. The Bank conducts a general
commercial banking business in its service area, emphasizing the banking needs
of individuals and small- to medium-sized businesses and professional concerns.

         The following discussion of the financial condition and results of
operations of the Company should be read in conjunction with the Company's
financial statements and related notes and other statistical information
included elsewhere herein.

Results of Operations

         Net income for the Company for the three months ended March 31, 1998,
was $27,599, compared to $63,756 during the corresponding period of 1997. The
decrease in earnings can be attributed primarily to an increase in noninterest
expenses which have grown as the Bank has expanded, and the retarded growth in
net interest income which was the result of placing one loan in the amount of
$2.3 million on non-accrual status as of the quarter end. Lost interest on this
nonperforming asset totals approximately $19,500 each month. The loan is fully
secured by real estate and is guaranteed by the U.S. Department of Agriculture
Rural Community & Development Program. The U.S. Government is responsible for
80% of any deficiency after liquidation of the collateral. Collection efforts on
this loan are progressing. Management estimates that the Bank's risk of loss on
this loan is approximately $116,000.

         The Bank's loan portfolio increased from $29.9 million at March 31,
1997, to $34.8 million at March 31, 1998. The Bank's provision for loan losses
was $36,533 for the quarter ended March 31, 1998, compared to $21,858 for the
quarter ended March 31, 1997. The allowance for loan losses was $387,400 at
March 31, 1998, or 1.10% of total loans, compared to $378,000 at December 31,
1997, or 1.08% of total loans. The level of the allowance for loan losses
represents management's current estimate of future losses in the loan portfolio;
however, there can be no assurance that loan losses in future periods will not
exceed the allowance for loan losses or that additional increases in the
allowance will not be required.

         Noninterest expense increased $25,864, or 8.1%, to $344,234 for the
quarter ended March 31, 1998, from $318,370 for the quarter ended March 31,
1997. This increase was primarily related to the increase in salaries and
benefits of $30,132. This increase in salaries and benefits was primarily due to


                                       5
<PAGE>   7
adding two new full-time positions in the second quarter of 1997. Offsetting the
increase in salaries and benefits, occupancy expenses decreased $7,008 due to
rent income received of approximately $9,500 from two tenants.

         Return on average assets and average equity, on an annualized basis,
for the quarter ended March 31, 1998, were .29% and 3.19%, respectively,
compared to .77% and 7.95%, respectively, for the same quarter of 1997. Earnings
per share on a fully diluted basis for the quarters ended March 31, 1998, and
March 31, 1997, amounted to $0.05 and $0.11, respectively.

         The Company's assets ended the first quarter of 1998 at $43.8 million,
an increase of 2.5% from $42.7 million at December 31, 1997. This increase can
be attributed primarily to the increase in the Bank's deposits which resulted in
the increase of approximately $600,000 in federal funds sold and the increase of
approximately $364,000 in cash and due from banks. Total deposits ended the
quarter at $39.2 million, up 2.8% from $38.1 million at December 31, 1997. At
March 31, 1998, the Company's loan to deposit ratio was 89.0%, compared to
91.05% at December 31, 1997.

         Management expects that its 1998 income will exceed expenses. Although
management expects that the Company's current profitably will continue, future
events, such as an unanticipated deterioration in the loan portfolio, could
reverse this trend. Management's expectations are based on management's best
judgment and actual results will depend on a number of factors that cannot be
predicted with certainty and thus fulfillment of management's expectations
cannot be assured.

Liquidity and Sources of Capital

         The $1.1 million increase in deposits from December 31, 1997, to March
31, 1998, is primarily reflected in the increase of approximately $600,000 in
federal funds sold and the increase of approximately $364,000 in cash and due
from banks. The Company's primary source of liquidity is cash on hand plus
short-term investments. At March 31, 1998, the Company's liquid assets totaled
$7.0 million, or 16.0% of total assets, compared to $6.0 million, or 14.1% of
total assets, at December 31, 1997. Another source of liquidity is the
$3,500,000 secured line of credit the Company has from the Federal Home Loan
Bank, the $1,000,000 unsecured line of credit the Company has from a
correspondent bank, and the $1,500,000 secured line of credit the Company has
from another correspondent bank, of which $675,000 of the $1,500,000 line of
credit is pledged to secure repurchase agreements. If additional liquidity is
needed, the Bank will sell participations in its loans.

         The capital of the Company and the Bank exceeded all prescribed
regulatory capital guidelines at March 31, 1998. At March 31, 1998, the Tier 1
leverage ratio for the Bank was 9.19%. At March 31, 1998, the Bank had a
risk-weighted total capital ratio of 12.99%, and a Tier 1 risk-weighted capital
ratio of 11.83%. The Company expects that its current capital and short-term
investments will satisfy the Company's cash requirements for the foreseeable
future. However, no assurance can be given in this regard as rapid growth,
deterioration in the loan quality or poor earnings, or a combination of these
factors, could change the Company's capital position in a relatively short
period of time.

 Year 2000 Issues

         The Company uses a third-party data processor for most of its
accounting functions. The processor has implemented many changes in preparation
for the year 2000 ("Year 2000"). Testing should be complete by the end of 1998.
The Company also has a number of portable computers, most of which, due to their
age, are Year 2000 compliant. Management expects no significant costs to get its
systems Year 2000 compliant. The largest Year 2000 exposure to most banks is the
preparedness of 


                                        6
<PAGE>   8
the customers of the banks. Management is addressing with its customers the
possible consequences of not being prepared for Year 2000. Should large
borrowers not sufficiently address this issue, the Company may experience an
increase in loan defaults. The amount of potential loss from this issue is not
quantifiable. Management is attempting to reduce this exposure by educating its
customers.

                                     PART II
                                OTHER INFORMATION

ITEM 1.  LEGAL PROCEEDINGS.

         There are no material pending legal proceedings to which the Company or
the Bank is a party or of which any of their property is the subject.

ITEM 2.  CHANGES IN SECURITIES.

         On March 5, 1998, a director and officer of the Company exercised
options to acquire 150 shares of the Company's Common Stock. The options had an
exercise price of $10 per share and thus the Company received $1,500. The Common
Stock issued pursuant to the exercise of the options represents unregistered
securities, which issuance was considered to be exempt from registration under
the Securities Act of 1933 pursuant to Section 4(2) as a transaction by an
issuer not involving any public offering.

ITEM 3.  DEFAULTS UPON SENIOR SECURITIES.

         Not applicable.

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

         There were no matters submitted to security holders for a vote during
the quarter ended March 31, 1998.

ITEM 5.  OTHER INFORMATION.

         Effective May 1, 1998, R. Michael S. Menzies assumed the positions of
President of the Company and President and Chief Executive Officer of the Bank.
Mr. Menzies, age 51, has over twenty-five years of experience in top tier
regional commercial banking and independent community banking environments. He
has previously served as Chairman of the Board and President of First Bank of
Frederick and Chief Executive Officer of First Frederick Financial Company.
Between 1989 and 1998, First Bank of Frederick grew from $6 million in assets to
$100 million in assets with profits exceeding $1 million and return on equity of
15%. On two occasions, the Small Business Administration recognized First Bank
loan officers as the Small Business Lenders of the Year. Mr. Menzies and his
wife of twenty-nine years have been active in community volunteer activities in
Frederick and Easton, Maryland, and will reside in the Village of Cooks Hope,
Easton, Maryland.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K.

         (a)      Exhibits.

                  3.1      Articles of Incorporation of the Company
                           (incorporated by reference to Exhibit 3.1 of
                           Registration Statement on Form S-18, File No.
                           33-43317).


                                       7
<PAGE>   9
                  3.2      Bylaws of the Company (incorporated by reference to
                           Exhibit 3.2 of Registration Statement on Form S-18,
                           File No. 33-43317).

                  10.1     Employment Agreement dated July 22, 1991, between the
                           Company and Thomas P. McDavid (incorporated by
                           reference to Exhibit 10.1 of Registration Statement
                           on Form S-18, File No. 33-43317).

                  10.2     Easton Bancorp, Inc. 1991 Stock Option Plan
                           (incorporated by reference to Exhibit 10.2 of
                           Registration Statement on Form S-18, File No.
                           33-43317).

                  10.3     Form of Warrant Agreement (incorporated by reference
                           to Exhibit 10.3 of Registration Statement on Form
                           S-18, File No. 33-43317).

                  10.4     Agreement with Thomas P. McDavid dated March 6, 1998.

                  11.1     Computation of Earnings Per Share.

                  27.1     Financial Data Schedule (for SEC use only).

         (b)      Reports on Form 8-K.

                  On March 16, 1998, the Company filed a Current Report on Form
                  8-K announcing that Thomas P. McDavid, the President and a
                  director of the Company and the President, Chief Executive
                  Officer and a director of the Bank, had resigned as an officer
                  and director of the Company and the Bank and terminated his
                  employment with the Bank. As stated in the Form 8-K, Delia B.
                  Denny, the Senior Vice President of the Bank, was appointed to
                  serve on an interim basis as the President and Chief Executive
                  Officer of the Bank. The Company did not appoint an interim
                  President of the Company.






                                       8
<PAGE>   10
                                   SIGNATURES


         In accordance with the requirements of the Exchange Act, the registrant
caused this report to be signed on its behalf by the undersigned, thereunto duly
authorized.

                                            EASTON BANCORP, INC.
                                          --------------------------------------
                                               (Registrant)



Date:    May 13, 1998                     By: /s/ W. David Hill
       --------------------                   ----------------------------------
                                                  W. David Hill
                                                  Chairman of the Board



Date:    May 13, 1998                     By: /s/ Pamela A. Mussenden
       --------------------                   ----------------------------------
                                                  Pamela A. Mussenden
                                                  Assistant Treasurer
                                                  (Principal Financial Officer)






                                       9
<PAGE>   11
                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>
Exhibit                                                                            Sequential
Number                              Description                                    Page Number
------                              -----------                                    -----------
<S>      <C>                                                                       <C>
3.1      Articles of Incorporation of the Company (incorporated by reference to
         Exhibit 3.1 of Registration Statement on Form S-18, File No. 33-43317).

3.2      Bylaws of the Company (incorporated by reference to Exhibit 3.2 of
         Registration Statement on Form S-18, File No. 33-43317).

10.1     Employment Agreement dated July 22, 1991, between the Company and
         Thomas P. McDavid (incorporated by reference to Exhibit 10.1 of
         Registration Statement on Form S-18, File No. 33-43317).

10.2     Easton Bancorp, Inc. 1991 Stock Option Plan (incorporated by reference
         to Exhibit 10.2 of Registration Statement on Form S-18, File No.
         33-43317).

10.3     Form of Warrant Agreement (incorporated by reference to Exhibit 10.3 of
         Registration Statement on Form S-18, File No. 33-43317).

10.4     Agreement with Thomas P. McDavid dated March 6, 1998.

11.1     Computation of Earnings Per Share.

27.1     Financial Data Schedule (for SEC use only).
</TABLE>






                                       10